Add Request a quote widget in Storefront theme header

To replace the cart widget with the YITH Request a Quote for WooCommerce widget in Storefront theme header, please, follow these steps:

First of all, you have to add this code into the functions.php file of Storefront (better if it is a child):

//Add our custom widget
add_action( 'storefront_header', 'storefront_header_raq', 60 );
if ( ! function_exists( 'storefront_header_raq' ) ) {

    function storefront_header_raq() {
        if ( storefront_is_woocommerce_activated() ) {
            echo do_shortcode( '[yith_ywraq_mini_widget_quote]' );
        }
    }
}

//set footer link
add_filter( 'storefront_handheld_footer_bar_links', 'set_raq_link_footer' );
if ( ! function_exists( 'set_raq_link_footer' ) ) {

    function set_raq_link_footer( $links ) {

        unset( $links['cart'] );
        $links['raq'] = array(
            'priority' => 30,
            'callback' => 'storefront_handheld_footer_bar_raq_link',
        );

        return $links;

    }

}

//render footer link
if ( ! function_exists( 'storefront_handheld_footer_bar_raq_link' ) ) {

    function storefront_handheld_footer_bar_raq_link() {
        ?>
        <a class="ywraq_number_items_container" href="<?php echo esc_url( YITH_Request_Quote()->get_raq_page_url() ) ?>">
            <?php echo do_shortcode( '[yith_ywraq_number_items class="ywraq_number_items" show_url="no" item_name="" item_plural_name=""]' ); ?>
        </a>
        <?php
    }

}

Now, the new widget is visible in the header but you have to adjust its style. So, by adding the following snippet, you can make it look like the cart widget:

//customize style
add_action( 'wp_enqueue_scripts', 'my_yith_wraq_style', 25 );
if ( ! function_exists( 'my_yith_wraq_style' ) ) {
    function my_yith_wraq_style() {

        $storefront_customizer = new Storefront_Customizer();
        $storefront_theme_mods = $storefront_customizer->get_storefront_theme_mods();

        $css = '
.widget_ywraq_mini_list_quote {
    width: 21.7391304348%;
    float: right;
    margin: 0 !important;
}

.yith-ywraq-list-widget-wrapper .raq-info {
    margin: 0;
    padding: 1.618em 0;
    border: 0 none;
}

.yith-ywraq-list-widget-wrapper .raq_label{
   display:block;
}

.yith-ywraq-list-widget-wrapper .raq_label:after {
    -webkit-font-smoothing: antialiased;
    -moz-osx-font-smoothing: grayscale;
    display: inline-block;
    font-style: normal;
    font-variant: normal;
    font-weight: normal;
    line-height: 1;
    vertical-align: -.125em;
    font-family: "Font Awesome 5 Free";
    font-weight: 900;
    line-height: inherit;
    vertical-align: baseline;
    content: "\f46d";
    height: 1em;
    float: right;
    line-height: 1.618;
}

.yith-ywraq-list-widget-wrapper .raq-info .handler-label {
    float: left;
    margin: 0 5px 0 0 
}

.yith-ywraq-list-wrapper {
    right: 0;
}

@media screen and (max-width:767px){

.widget_ywraq_mini_list_quote{
   display:none;
}

}


li.raq .ywraq_number_items_container{
    height: 4.235801032em;
    display: block;
    position: relative;
    text-indent: -9999px;
    z-index: 999;
    border-right: 1px solid rgba(255,255,255,.2);
}

li.raq .ywraq_number_items_container:before{
    -webkit-font-smoothing: antialiased;
    -moz-osx-font-smoothing: grayscale;
    display: inline-block;
    font-style: normal;
    font-variant: normal;
    font-weight: normal;
    line-height: 1;
    vertical-align: -.125em;
    font-family: "Font Awesome 5 Free";
    font-weight: 900;
    line-height: inherit;
    vertical-align: baseline;
    position: absolute;
    top: 0;
    left: 0;
    right: 0;
    bottom: 0;
    text-align: center;
    line-height: 2.618046972;
    font-size: 1.618em;
    text-indent: 0;
    display: block;
    cursor: pointer;
    content: "\f46d";
}

li.raq .ywraq_number_items_container div{
    text-indent: 0;
    display: block;
    width: 2em;
    height: 2em;
    line-height: 2;
    box-sizing: content-box;
    font-size: .75em;
    position: absolute;
    top: .875em;
    left: 50%;
    border-radius: 100%;
    border: 1px solid;
    background-color: ' . $storefront_theme_mods['header_link_color'] . ';
    color: ' . $storefront_theme_mods['header_background_color'] . ';
    border-color: ' . $storefront_theme_mods['header_background_color'] . ';
    }
 
';
        wp_add_inline_style( 'yith_ywraq_frontend', $css );

    }
}

Finally, remove the cart widget, with this snippet:

//remove cart widget
remove_action( 'storefront_header', 'storefront_header_cart', 60 );